Lens

A lens is a special optical tool that can gather or spread a light beam by changing its direction. This happens because of something called refraction.

A simple lens is just one piece of transparent material. A compound lens has many simple lenses put together along a line called an axis. We make lenses from things like glass or plastic. They are shaped by grinding, polishing, or molding.

A burning apparatus consisting of two biconvex lens

Lenses are important in many devices. You can find them in telescopes, binoculars, and cameras. They are also used in glasses to help people see better. This is useful for fixing vision problems like myopia and hypermetropia. A lens can make a picture by focusing light. This is different from a prism, which changes light’s direction but does not focus it.

History

See also: History of optics and Camera lens

Light being refracted by a spherical glass container full of water. Roger Bacon, 13th century

The word lens comes from the Latin name for the lentil plant, because early lenses looked like this seed. Ancient people may have used simple lenses for making fire or as decorations, but we do not know how often they used them to help see better.

One of the oldest known lenses, the Nimrud lens, dates back to the 7th century BCE. Over time, people learned to make better lenses for reading and for seeing far away. By the 1200s, spectacle glasses were being made in places like Italy, Venice, and Florence. Later, these skills helped create the microscope around 1595 and the telescope in 1608, both important tools for science.

Construction of simple lenses

Most lenses are round like balls. Their two sides can be curved outwards, curved inwards, or flat. The line joining the centers of the round shapes is called the lens axis, and it usually goes through the middle of the lens.

Lenses are grouped by the shape of their sides. A biconvex lens has both sides curved outwards. A biconcave lens has both sides curved inwards. If one side is flat, the lens is called plano-convex or plano-concave. Lenses with one curved outwards side and one curved inwards side are called meniscus lenses. These are often used in eyeglasses to help people see better.

A biconvex or plano-convex lens in air brings light together to a point behind the lens and is called a converging lens. A biconcave or plano-concave lens makes light spread out and is called a diverging lens. The distance from the lens to the point where the light meets is known as the focal length.

Sign convention for Gaussian lens equation
Parameter	Meaning	+ Sign	− Sign
s_o	The distance between an object and a lens.	Real object	Virtual object
s_i	The distance between an image and a lens.	Real image	Virtual image
f	The focal length of a lens.	Converging lens	Diverging lens
y_o	The height of an object from the optical axis.	Erect object	Inverted object
y_i	The height of an image from the optical axis	Erect image	Inverted image
M_T	The transverse magnification in imaging ( = the ratio of y_i to y_o ).	Erect image	Inverted image

Imaging properties

A lens can focus light to a special point called the focal point. If a light source is placed at this focal point, the lens can make the light rays spread out evenly. These actions help create images.

Single thin lens imaging with chief rays

There are rules that tell us where an image will form based on where the object is placed. For thin lenses, these rules can be shown with simple math. One key idea is that the distance from the object to the lens and the distance from the lens to the image are connected through the lens's focal length.

When an object is far away, the image forms at the focal point. If the object is close to the lens, the image can appear on the other side of the lens or even seem to be behind the lens, which we call a virtual image. Real images can be seen on screens, while virtual images can only be seen looking through the lens.

Images of Real Objects Formed by Thin Lenses
Lens Type	Object Location	Image Type	Image Location	Lateral Image Orientation	Image Magnification	Remark
Converging lens	∞ > S 1 > 2 f {\displaystyle \infty >S_{1}>2f}	Real	f	Inverted	Diminished
Converging lens	S 1 = 2 f {\displaystyle S_{1}=2f}	Real	S 2 = 2 f {\displaystyle S_{2}=2f}	Inverted	Same size
Converging lens	f	Real	∞ > S 2 > 2 f {\displaystyle \infty >S_{2}>2f}	Inverted	Magnified
Converging lens	S 1 = f {\displaystyle S_{1}=f}		± ∞ {\displaystyle \pm \infty }
Converging lens	S 1	Virtual	\| S 2 \| > S 1 {\displaystyle \vert S_{2}\vert >S_{1}}	Erect	Magnified	As an object moves toward the lens, the virtual image gets closer to the lens and the image size decreases.
Diverging lens	Anywhere	Virtual	\| S 2 \| \| S 2 \| {\displaystyle \vert S_{2}\vert \vert S_{2}\vert }	Erect	Diminished	As an object moves toward the lens, the virtual image gets closer to the lens and the image size increases.

Aberrations

Main article: Optical aberration

Lenses can’t make perfect images. They often cause some blurring or distortion, known as aberration. This happens because no lens is perfect. Different parts of a lens focus light differently. There are several common types of aberration that affect how clear an image looks.

Spherical aberration

Main article: Spherical aberration

Spherical aberration happens because easy-to-make lens shapes, like round curves, aren’t perfect for focusing light. Light beams far from the center of the lens focus in slightly different places than beams near the center. This can make images look blurry. Designers can reduce this problem by carefully choosing the curves of the lens.

Coma

Main article: Coma (optics)

Coma makes images look like little comets. It happens when an object isn’t straight in front of the lens. Light rays pass through at an angle. Rays through the center of the lens focus in one place, while rays through the edges focus elsewhere. This creates a flare-shaped blur. This can also be reduced by choosing the right curves for the lens.

Chromatic aberration

Main article: Chromatic aberration

Chromatic aberration occurs because a lens bends different colors of light by different amounts. This creates colorful edges around objects in an image. It can be lessened by combining two different types of glass in one lens, called an achromatic doublet, or by using special materials like fluorite, which bends light more evenly.

Other types of aberration

Other kinds of aberration include field curvature, barrel and pincushion distortion, and astigmatism.

Aperture diffraction

Even with perfect design, the way light spreads out when it passes through the lens opening, or aperture, can limit image quality. A diffraction-limited lens is one where this spreading of light is the main factor affecting the image.

Compound lenses

Simple lenses can make images blurry because of problems called optical aberrations. By putting two or more simple lenses together to make a compound lens, we can fix many of these problems. A compound lens is made of several simple lenses placed in a line. Each lens is made from materials that bend light a little differently.

When light goes through several lenses one after another, each lens changes the shape of the light beam a little. The first lens makes an image, and that image becomes the object for the next lens, and so on, until the last lens makes the final image we see. This way, each lens helps make the picture clearer and sharper.

Non spherical types

Cylindrical lenses curve in only one direction. They help focus light into a line or change the shape of light from a laser diode. Aspheric lenses have special shapes that make images clearer than regular lenses.

Fresnel lenses are thin and light. Their surface is split into narrow rings. Lenticular lenses are used in special printing. They create images that change when you look at them from different angles. Other types of lenses, like bifocal lenses, have different focal lengths in different parts.

Uses

A watch with a plano-convex lens over the date indicator

Lenses are used in many everyday items to help us see better and capture images. For example, they are used in eyeglasses and contact lenses to correct vision problems. They are also found in tools like magnifying glasses, binoculars, telescopes, microscopes, cameras, and projectors.

Lenses can also focus sunlight to a point strong enough to burn things. They are used in special devices to collect energy for solar power. Some radio systems use special lenses to help guide signals.